Where Is This Player's Money Going?

[Leonardo]

I want the boring equations. As for giving a rigorous proof, you didnt give any proof, let alone a rigorous one. Again, you are coming up with a bunch of qualitative arguments which may or may not be correct. Ill wait for the equations.
As for the big pot thing, Ill give an example that will make it crystal clear. If there is a billion dollars in the pot and you reach say the turn, where each of you have a thousand dollars, it makes no difference what your position is. If the pot is one dollar the position is worth a lot.

[PokrLikeItsProse]

[ QUOTE ]
I want the boring equations. As for giving a rigorous proof, you didnt give any proof, let alone a rigorous one. Again, you are coming up with a bunch of qualitative arguments which may or may not be correct. Ill wait for the equations.
As for the big pot thing, Ill give an example that will make it crystal clear. If there is a billion dollars in the pot and you reach say the turn, where each of you have a thousand dollars, it makes no difference what your position is. If the pot is one dollar the position is worth a lot.

[/ QUOTE ]

That's a pretty pointless example. When are you going to have a billion dollars in the pot in a limit hold em game when the bet size is a thousand dollars or less?

Here's one example. You have JdJs in the CO, button has Ad5c, SB has Qc2c, BB has Kh4d. If it is folded to you and you just limp and all call, and you will have a 34.62% chance of winning a pot that contains four small bets. If you raise and the Ad5c calls, you will have a 69.82% chance of winning a pot containing 5.5 small bets. If you raise and both the button and BB call, you have a 50.05% chance of winning a pot containing 6.5 small bets. And of course, there is a chance that everyone might fold to you and you pick up the blinds, which is not so bad a hand like JJ that is vulnerable to overcards.

Raising clearly increases your expected value in the hand than if you merely limp in. In the first case, on average you expect to win back 1.38 small bets when you limp in for a small bet. In the second case, you expect to win back 3.84 small bets for the price of putting in two small bets before the flop. In the third case, you expect to win back 3.25 small bets for every two small bets you put in. In the last case, you win the 1.5 small bets in the blinds.

In the unlikely event that you raise and get three callers, you expect to win back 2.77 small bets for every two bets you put in. Notice that you are +.38 if you just limp in but +.77 if you raise and everyone calls. You gain in value if you raise with the best hand and you also gain value by getting hands that could outdraw you to fold.